Sum of multinomial coefficient

Question

I want to show that $$\sum_{j,k,j+k\leq n} 3^{-n}\frac{n!}{j!k!(n-k-j)!}=1.$$ I tried to do it by induction, but this clearly seems the wrong approach because the denominator becomes very hard to deal with. I also tried to form a binomial coefficient so that I can perhaps use a formula, but this is also too complicated since I have to deal with the cases where $k \leq j$ and vice versa. This fact was made to seem obvious in papers I read so I believe it can be proven some way.